Search

Aggregation, as an operation of cartographic generalization, provides an effective means of abstracting the configuration of building features by combining them according to the scale reduction of the 2D map. Automating this design process effectively helps professional cartographers design both paper and digital maps, but finding the best aggregation result from the numerous combinations of building features has been a challenge. This paper presents a novel approach to assist cartographers in interactively designing the aggregation of building features in scale‐aware map visualization. Our contribution is to provide an appropriate set of candidates for the cartographer to choose from among a limited number of possible combinations of building features. This is achieved by collecting locally optimal solutions that emerge in the course of aggregation operations, formulated as a label cost optimization problem. Users can also explore better aggregation results by interactively adjusting the design parameters to update the set of possible combinations, along with an operator to force the combination of manually selected building features. Each cluster of aggregated building features is tightly enclosed by a concave hull, which is later adaptively simplified to abstract its boundary shapes. Experimental design examples and evaluations by expert cartographers demonstrate the feasibility of the proposed approach to interactive aggregation. [ABSTRACT FROM AUTHOR]

In recent years, neutrosophic theory has garnered increasing attention within scholarly circles due to its applicability in various domains. Within these domains, the field of decision-making has derived significant advantages from the progressions in neutrosophic theory. Notably, neutrosophic theory has made substantial contributions by advancing and offering a range of aggregation operators and information measures specifically designed for enhancing decision-making processes. In this context, this study aims to conduct a comprehensive bibliometric analysis of the current research landscape in the field of neutrosophic theory, with a specific focus on understanding its applications and development trends. Our analysis reveals that the scientific literature addresses neutrosophic theory in a diverse range of applications. This examination encompasses a scrutiny of key contributors, affiliated academic institutions, influential publications, and noteworthy journals within the neutrosophic domain. To achieve this, we have curated a dataset comprising scholarly papers retrieved from Clarivate Analytics' Web of Science Core Collection database, employing keywords closely aligned with neutrosophic theory and its applications, spanning a specified timeframe starting from the year in which the first paper on neutrosophic theory was published, namely, from 2005 until 2022. Our findings underscore sustained and robust scholarly interest in neutrosophic theory, characterized by a considerable high annual growth rate of 43.74% during the specified period. Additionally, our investigation delves into the identification and analysis of pivotal keywords and emerging trends, shedding light on prominent research trajectories within this domain. Furthermore, we elucidate collaborative networks among authors, their academic affiliations, and the global distribution across diverse countries and territories, providing valuable insights into the worldwide proliferation of neutrosophic research and applications. Employing n-gram analysis techniques across titles, keywords, abstracts, and keyword-plus fields unveils a multitude of applications where neutrosophic theory plays a central role. The analysis culminates in a review of globally cited documents and a comprehensive discussion highlighting the significance of neutrosophic theory in contemporary research and problem-solving contexts. [ABSTRACT FROM AUTHOR]

When information is incomplete or uncertain, Fermatean hesitant fuzzy sets (FHFSs) can provide more information to help decision-makers deal with more complex problems. Typically, determining attribute weights assumes that each attribute has a fixed influence. Introducing probability information can enable one to consider the stochastic nature of evaluation data and better quantify the importance of the attributes. To aggregate data by considering the location and importance degrees of each attribute, this paper develops a Fermatean hesitant fuzzy multi-attribute decision-making (MADM) method with probabilistic information and an ordered weighted averaging (OWA) method. The OWA method combines the concepts of weights and sorting to sort and weigh average property values based on those weights. Therefore, this novel approach assigns weights based on the decision-maker's preferences and introduces probabilities to assess attribute importance under specific circumstances, thereby broadening the scope of information expression. Then, this paper presents four probabilistic aggregation operators under the Fermatean hesitant fuzzy environment, including the Fermatean hesitant fuzzy probabilistic ordered weighted averaging/geometric (FHFPOWA/FHFPOWG) operators and the generalized Fermatean hesitant fuzzy probabilistic ordered weighted averaging/geometric (GFHFPOWA/GFHFPOWG) operators. These new operators are designed to quantify the importance of attributes and characterize the attitudes of decision-makers using a probabilistic and weighted vector. Then, a MADM method based on these proposed operators is developed. Finally, an illustrative example of selecting the best new retail enterprise demonstrates the effectiveness and practicality of the method. [ABSTRACT FROM AUTHOR]

Big data pertains to extensive and intricate compilations of information that necessitate the implementation of proficient and cost-effective evaluation and analysis tools to derive insights and support decision making. The Fermatean fuzzy set theory possesses remarkable capability in capturing imprecision due to its capacity to accommodate complex and ambiguous problem descriptions. This paper presents the study of the concepts of dynamic ordered weighted aggregation operators in the context of Fermatean fuzzy environment. In numerous practical decision making scenarios, the term "dynamic" frequently denotes the capability of obtaining decision-relevant data at various time intervals. In this study, we introduce two novel aggregation operators: Fermatean fuzzy dynamic ordered weighted averaging and geometric operators. We investigate the attributes of these operators in detail, offering a comprehensive description of their salient features. We present a step-by-step mathematical algorithm for decision making scenarios in the context of proposed methodologies. In addition, we highlight the significance of these approaches by presenting the solution to the decision making problem and determining the most effective big data analytics platform for YouTube data analysis. Finally, we perform a thorough comparative analysis to assess the effectiveness of the suggested approaches in comparison to a variety of existing techniques. [ABSTRACT FROM AUTHOR]

Belief and plausibility functions based on evidence theory (ET) have been widely used in managing uncertainty. Various generalizations of ET to fuzzy sets (FSs) have been reported in the literature, but no generalization of ET to q-rung orthopair fuzzy sets (q-ROFSs) has been made yet. Therefore, this paper proposes a novel, simple, and intuitive approach to distance and similarity measures for q-ROFSs based on belief and plausibility functions within the framework of ET. This research addresses a significant research gap by introducing a comprehensive framework for handling uncertainty in q-ROFSs using ET. Furthermore, it acknowledges the limitations inherent in the current state of research, notably the absence of generalizations of ET to q-ROFSs and the challenges in extending belief and plausibility measures to certain aggregation operators and other generalizations including Hesitant fuzzy sets, Bipolar fuzzy sets, Fuzzy soft sets etc. Our contribution lies in the proposal of a novel approach to distance and similarity measures for q-ROFSs under ET, utilizing Orthopairian belief and plausibility intervals (OBPIs). We establish new similarity measures within the generalized ET framework and demonstrate the reasonability of our method through useful numerical examples. Additionally, we construct Orthopairian belief and plausibility GRA (OBP-GRA) for managing daily life complex issues, particularly in multicriteria decision-making scenarios. Numerical simulations and results confirm the usability and practical applicability of our proposed method in the framework of ET. [ABSTRACT FROM AUTHOR]

Chinese family farms are continuously expanding; they are also facing various business risks that lead to a shorter lifespan. This paper constructed a family farm business risk assessment model that combined a hesitant fuzzy linguistic term sets (HFLTS) model with a hesitant fuzzy weighted average (HFWA) operator. On the basis of the factor analysis, this study built a family farm indicator system that included the natural, technical, market, policy, society, and management risk. The HFLTS was used for the assessment of weights in pairwise comparison matrices, and the HFWA operator was used as an aggregation operator to calculate the business risk score of family farms. For our case study, a method comparison analysis was also performed to check the validity of the results obtained by our risk assessment model. [ABSTRACT FROM AUTHOR]

The Temporal Complex Neutrosophic Set (TCNS) is a powerful extension of the Neutrosophic theory, and TCNS has added advantage to represents uncertain, indeterminate, inconsistent and time related factors. In the literature TCNS has been used for multi-criteria decision-making problems, especially in the time-aware systems. In order to tackle effectively decision-making problems in the TCNS environment effectively, it is crucial to make suite aggregation operators that enable decision makers to process preferences in a nuanced manner. In this paper, we introduce novel TCNS aggregation operators based on Aczel and Alsina t-norm and t-conorm using Aczel-Alsina operations, and we propose a multi-criteria decision-making model that utilizes those operators for TCNS-based multi criteria decision making problems (MCDMs). Theorytically, the soundness and completeness of new aggregation operators are proved, and to demonstrate the practicality and effectiveness of our model a real world case study for tourist destination selection in Vietnam is completed along with analysis. The result proved the application potential of the proposal to solve the time-related MCDMs in practical, such as creating a MCDM model for tourist destination selection. [ABSTRACT FROM AUTHOR]

The extensions of ordinary fuzzy sets are problematic because they require decimal numbers for membership, non-membership and indecision degrees of an element from the experts, which cannot be easily determined. This will be more difficult when three or more digits' membership degrees have to be assigned. Instead, proportional relations between the degrees of parameters of a fuzzy set extension will make it easier to determine the membership, non-membership, and indecision degrees. The objective of this paper is to present a simple but effective technique for determining these degrees with several decimal digits and to enable the expert to assign more stable values when asked at different time points. Some proportion-based models for the fuzzy sets extensions, intuitionistic fuzzy sets, Pythagorean fuzzy sets, picture fuzzy sets, and spherical fuzzy sets are proposed, including their arithmetic operations and aggregation operators. Proportional fuzzy sets require only the proportional relations between the parameters of the extensions of fuzzy sets. Their contribution is that these models will ease the use of fuzzy set extensions with the data better representing expert judgments. The imprecise definition of proportions is also incorporated into the given models. The application and comparative analyses result in that proportional fuzzy sets are easily applied to any problem and produce valid outcomes. Furthermore, proportional fuzzy sets clearly showed the role of the degree of indecision in the ranking of alternatives in binomial and trinomial fuzzy sets. In the considered car selection problem, it has been observed that there are minor changes in the ordering of intuitionistic and spherical fuzzy sets. [ABSTRACT FROM AUTHOR]

Aggregation operators have the important application in any fields where the fusion of information is processed. The dominance relation between two aggregation operators is linked to the fusion of fuzzy relations, indistinguishability operators and so on. In this paper, we deal with the weak dominance relation between two aggregation operators which is closely related with the dominance relation. Weak domination of isomorphic aggregation operators and ordinal sum of conjunctors is presented. More attention is paid to the weak dominance relation between ordered weighted averaging operators and Lukasiewicz t-norm. Furthermore, the relationships between weak dominance and some functional inequalities of aggregation operators are discussed. [ABSTRACT FROM AUTHOR]

The main goal of informal computing is to overcome the limitations of hypersensitivity to defects and uncertainty while maintaining a balance between high accuracy, accessibility, and cost-effectiveness. This paper investigates the potential applications of intuitionistic fuzzy sets (IFS) with rough sets in the context of sparse data. When it comes to capture uncertain information emanating from both upper and lower approximations, these intuitionistic fuzzy rough numbers (IFRNs) are superior to intuitionistic fuzzy sets and pythagorean fuzzy sets, respectively. We use rough sets in conjunction with IFSs to develop several fairly aggregation operators and analyze their underlying properties. We present numerous impartial laws that incorporate the idea of proportionate dispersion in order to ensure that the membership and non-membership activities of IFRNs are treated equally within these principles. These operations lead to the development of the intuitionistic fuzzy rough weighted fairly aggregation operator (IFRWFA) and intuitionistic fuzzy rough ordered weighted fairly aggregation operator (IFRFOWA). These operators successfully adjust to membership and non-membership categories with fairness and subtlety. We highlight the unique qualities of these suggested aggregation operators and investigate their use in the multi-attribute decision-making field. We use the intuitionistic fuzzy rough environment's architecture to create a novel strategy in situation involving several decision-makers and non-weighted data. Additionally, we developed a novel technique by combining the IFSs with quaternion numbers. We establish a unique connection between alternatives and qualities by using intuitionistic fuzzy quaternion numbers (IFQNs). With the help of this framework, we can simulate uncertainty in real-world situations and address a number of decision-making problems. Using the examples we have released, we offer a sophisticated and systematically constructed illustrative scenario that is intricately woven with the complexity of medical evaluation in order to thoroughly assess the relevance and efficacy of the suggested methodology. [ABSTRACT FROM AUTHOR]

The highly dynamic nature of the real-world environment poses significant challenges for electric bus system operations (EBSOs), which are prone to serious accidents due to their complexity and a wide variety of risk factors. The accidents are often the result of ignoring the most serious risk sources because of a lack of comprehensive risk assessments. Therefore, this paper proposes an improved failure mode and effects analysis (FMEA) multicriteria group decision-making model to ensure the reliability and safety of EBSOs. First, an expert group is invited to evaluate the risk failure modes (FMs) of the EBSOs and transform them into a normal wiggly hesitant fuzzy set (NWHFS) form. Because the risk assessment process involves a large number of team members with different backgrounds, the experts are grouped based on scoring function values using the K-medoids clustering technique. Then, the evaluation values of the expert group are integrated using the normal hesitant fuzzy weighted geometric (NWHFWG) aggregation operator to obtain the final aggregation matrix, and the weights of the three criteria of occurrence (O), severity (S) and detection (D) are determined for each FM via the CCSD method. Finally, considering the cross-correlation between factors within the system, the relationships between FMs are analyzed, and their impact and importance are quantified using the gray correlation-based DEMATEL method, followed by the final ranking of the FMs using regret theory and the PROMETHEE II methodology to achieve a rational allocation of resources. The results are analyzed with sensitivity and comparative analyses to illustrate the superiority of the model. [ABSTRACT FROM AUTHOR]

A T-spherical uncertain linguistic set (TSULS) is not only an expanded form of the T-spherical fuzzy set and the uncertain linguistic set but can also integrate the quantitative judging ideas and qualitative assessing information of decision-makers. For the description of complex and uncertain assessment data, TSULS is a powerful tool for the precise description and reliable processing of information data. However, the existing multi-attribute border approximation area comparison (MABAC) method has not been studied in TSULS. Thus, the goal of this paper is to extend and improve the MABAC method to tackle group decision-making problems with completely unknown weight information in the TSUL context. First, the cross-entropy measure and the interactive operation laws for the TSUL numbers are defined, respectively. Then, the two interactive aggregation operators for TSUL numbers are developed, namely T-spherical uncertain linguistic interactive weighted averaging and T-spherical uncertain linguistic interactive weighted geometric operators. Their effective properties and some special cases are also investigated. Subsequently, a new TSULMAGDM model considering the DM's behavioral preference and psychology is built by integrating the interactive aggregation operators, the cross-entropy measure, prospect theory, and the MABAC method. To explore the effectiveness and practicability of the proposed model, an illustrative example of Sustainable Waste Clothing Recycling Partner selection is presented, and the results show that the optimal solution is h3. Finally, the reliable, valid, and generalized nature of the method is further verified through sensitivity analysis and comparative studies with existing methods. [ABSTRACT FROM AUTHOR]

The ordered weighted averaging (OWA) operator was proposed by Yager back in 1988 and constitutes a parameterized family of aggregation functions between the minimum and the maximum. The purpose of this paper is to perform a bibliometric review of this aggregation operator during the last 35 years through the Web of Science (WoS) Core Collection database and the Visualization of Similarities (VOS) viewer software. The results show that the OWA operator is an increasingly popular aggregation operator, especially in Computer Science. The results also allow the assertion that Yager, as expected, is still the most influential and productive author. Moreover, the study reveals that institutions from over 80 countries have contributed to OWA research, highlighting the high presence of Chinese universities and the emergence of Pakistani ones. Other interesting findings are presented to provide a comprehensive and up-to-date analysis of the OWA operator literature. [ABSTRACT FROM AUTHOR]

Uncertainty, imprecise, incomplete, and inconsistent information can be found in many real-life systems and may cause more complex problems. A neutrosophic set is an effective and useful tool to describe problems with Uncertainty, imprecise, incomplete, and inconsistent information. The neutrosophic set is characterized by three independent degrees namely the truth-membership degree (T), indeterminacy-membership degree (I), and falsity-membership degree (F). In this paper, we present an extension of the VIKOR method for the solution of multi-criteria decision-making problems, namely neutrosophic set-VIKOR (NS-VIKOR) in a refined neutrosophic environment. The weight of each decision-maker is considered a singlevalued neutrosophic number. The criteria for the weight of every decision-maker are also considered neutrosophic numbers. An aggregation operator is used to combine all decision-makers' opinions into a single opinion for a rating between criteria and alternatives. Euclidean distances from the positive and negative ideal solutions are calculated to construct relative closeness coefficients. Lastly, an illustrative example of tablet selection is provided to show the applicability of the proposed VIKOR approach. [ABSTRACT FROM AUTHOR]

Intuitionistic fuzzy sets aims at taking the hesitancy of an expert into account in assigning a membership degree or a non-membership degree. The direct assignment of decimal numbers for membership and non-membership degrees of an element in intuitionistic fuzzy sets is not practical. Besides, the assigned degrees are generally composed of one digit or at most two digits after dot. This problem has not been addressed as much as it deserves in the literature. The hypothesis of the paper is that the determination of proportional relationships between membership and non-membership degrees is more appropriate than the direct assignment to obtain the degrees. Proportional intuitionistic fuzzy (PIF) sets require only the proportion relations between an intuitionistic fuzzy set's parameters. The accuracy of the results obtained with multi-criteria decision-making models definitely depends on how accurately the membership degrees are determined. In this paper, we extend Combinative distance-based assessment (CODAS) method by using single-valued proportional intuitionistic fuzzy sets. We compare the proposed PIF CODAS method with ordinary fuzzy CODAS method. A cloud service provider selection problem is handled to show the validity of the proposed PIF CODAS method. Additionally, a comparative analysis and a sensitivity analysis together with a discussion are presented. [ABSTRACT FROM AUTHOR]

This paper aims to support decision-makers improve their ability to accurately capture and represent their judgment in a wide range of situations. To do this, we propose a new type of fuzzy set called a p , q -cubic quasi-rung orthopair fuzzy set ( p , q -CQOFS). The p , q -CQOFS allows for a more flexible and detailed expression of incomplete information through the use of an additional parameter. The paper describes the concept of p , q -CQOFS and its relationship to other types of fuzzy sets, introduces score and accuracy functions for p , q -CQOFS and analyzes some of its mathematical properties, defines the Hamming distance measure between two p , q -CQOFSs and examines some of its important properties, investigates the basic operations of p , q -CQOFSs and extends these laws to aggregation operators, and introduces weighted averaging and geometric aggregation operators for combining p , q -cubic quasi-rung orthopair fuzzy data. [ABSTRACT FROM AUTHOR]

The ability of fuzzy set theory to offer a mathematical framework for the integration of arbitrary categories represented by membership functions is one of its most alluring aspects. But complexity arises when the number of criteria to be considered increases. In this paper, we propose a new concept called 'ordered weighted aggregation operators on multiple sets', by which the difficulty in considering the choices is minimized. This paper begins with the introduction of aggregation operators and ordered weighted aggregation operators in multiple sets. Along with certain key findings, a theoretical discussion based on them has also been made. Considering all the theories discussed, an application in personnel selection has been depicted in detail. The idea of dual aggregation operators on multiple sets has also been briefly introduced. [ABSTRACT FROM AUTHOR]

With the ever increasing interconnectedness among countries and industries, globalization has empowered economies and promoted international trade, capital flow and labor mobility, leading to improved products and services. However, the growing interdependence has also propelled an inherent reliance on joint cooperation which has considerably influenced the complexity of global value chains (GVCs). This plays a significant role in policy decisions, raising questions about trade risks that originate from such interdependence. In this paper, we study the impact of network linkage disturbances on the output supply and input demand of countries. We model the network interconnectedness of countries according to the latest 2016 release of the World Input–Output Database (WIOD) that includes data tables for the period 2000-2014 covering 43 countries as well as a model for the Rest of the World (ROW). We assess the shock distributions across the world economy by quantifying the changes in the network linkages using sensitivity analysis. Our contribution is in the definition of a shock tensor with the purpose of evaluating the impact of link sensitivity. The shock tensor is a straightforward yet comprehensive tool that allows us to obtain ample results at various levels of granularity when combining it with aggregation operators. Our study introduces a novel methodology that enables us to acquire input and output link sensitivities for all country pairings when an economic shock initiates or concludes within a country of interest. This innovative approach also facilitates the analysis of evolving trends in these link sensitivities, providing a comprehensive understanding of the dynamics of shock propagation across the global network. Taking advantage of the time-series nature of the WIOD, our results reveal illustrative visualizations and quantative measures that characterize patterns of shock distribution and relationships among countries throughout the period from 2000 to 2014. Our methodology and results not only uncover valuable trends but also establish a structured approach to better understand the aggregate effects of shock distributions. Thus, this study could be helpful for policy makers to assess trade relationships between countries and obtain quantitative insights for making informed decisions as well as explore the overall state of the globalization as a whole. [ABSTRACT FROM AUTHOR]

Circular q-rung orthopair fuzzy sets (FSs) were recently considered as an extension of q-rung orthopair FSs (q-ROFSs), circular intuitionistic FSs (Cir-IFSs), and circular Pythagorean FSs (Cir-PFSs). However, they are only considered for some simple algebraic properties. In this paper, we advance the work on circular q-ROFSs (Cirq-ROFSs) in Dombi aggregation operators (AOs) with more mathematical properties of algebraic laws. These include the circular q-rung orthopair fuzzy (Cirq-ROF) Dombi weighted averaging (Cirq-ROFDWA), Cirq-ROF Dombi ordered weighted averaging (Cirq-ROFDOWA), Cirq-ROF Dombi weighted geometric (Cirq-ROFDWG), and Cirq-ROF Dombi ordered weighted geometric (Cirq-ROFDOWG) operators. Additionally, we present the properties of idempotency, monotonicity, and boundedness for the proposed operators. In the context of artificial intelligence, symmetry analysis plays a significant and efficient role that can refer to several aspects. Thus, to compute the major aspect, we identify the multi-attribute decision-making (MADM) technique based on the proposed operators for Cirq-ROF numbers (Cirq-ROFNs) to enhance the worth of the evaluated operators. Finally, we use some existing techniques for comparison to our results to show the validity and supremacy of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, an interval Air Quality Index (AQI) combination prediction model based on EEMD, VMD, and the weighted power average (WPA) operator is proposed. EEMD and VMD decompose complex AQI data effectively, while WPA operator reasonably aggregates the prediction results of different models. We validate the effectiveness of the proposed model using Shenzhen's daily interval AQI. Furthermore, three kinds of prediction models are compared with the proposed model to highlight its advantages from various perspectives. The results show that the introduction of data decomposition methods significantly improves the model's prediction accuracy, WPA operator further enhances the model's prediction capability, and the incorporation of EEMD and VMD enables the proposed model to have stronger feature extraction capabilities for complex time series. As a result, the model proposed in this paper demonstrates strong generalization ability and prediction accuracy, making it applicable not only for air quality prediction but also for other domains such as economics and environment. [ABSTRACT FROM AUTHOR]

Improving a risk assessment technique for the problem of cyber security is required to modify the technique's capability to identify, evaluate, assess, and mitigate potential cyber threats and ambiguities. The major theme of this paper is to find the best strategy to improve and refine the cyber security risk assessment model. For this, we compute some operational laws for bipolar complex fuzzy soft (BCFS) sets and then propose the BCFS weighted averaging (BCFSWA) operator, BCFS ordered weighted averaging (BCFSOWA) operator, BCFS weighted geometric (BCFSWG) operator, and BCFS ordered weighted geometric (BCFSOWG) operator. Furthermore, we give their properties, such as idempotency, monotonicity, and boundedness. Additionally, we improve the risk assessment technique for the cyber security model based on the proposed operators. We illustrate the technique of multi-attribute decision-making (MADM) problems for the derived operators based on BCFS information. Finally, we compare our ranking results with those of some existing operators for evaluating and addressing the supremacy, validity, and efficiency of these operators under BCFS information. [ABSTRACT FROM AUTHOR]

Crowdfunding is a web-based financing scheme which aims to generate initial capital for startups. Nowadays, there are numerous programs which face the shortage in capital has already launching by crowdfunding. Meanwhile, there are always lots of potential investors who are puzzled by their choices and are thus cannot join them. In this paper, an assessment framework of crowdfunding projects founded on the three-way decision (TWD) is offered to solve the issue. The fuzziness and uncertainty in the evaluation information are the major factors affecting the accuracy of the output and the Fermatean fuzzy sets (FFS) of the proposed model conquers the problem. A Preference Selection Index - Standard Deviation Bayesian method is arranged to determine objective attribute weights with the precise and reliable data. Traditional fuzzy aggregation operators do not perform well in extreme and contradictory information processing situations, and FFS - evidence reasoning methodology (ERM) is proposed to gather messages, while the conditional probability is exported from the similarity metric. Improved FFS objective relative utility function supports TWD classifications and rankings, and the TWD-SAHARA utility function offers non-linear benefits tailored to human psychology. The proposed FF-PSI-SD-ERM-TWD has been utilized on eight crowdsourcing projects, and its effectiveness has been proven by sensitivity analysis and the results comparison. [ABSTRACT FROM AUTHOR]

In multi-attribute group decision-making (MAGDM), the attributes can be placed into independent groups based on their properties through partitioning. First, the partitioned dual Hamy mean (PDHM) operator is introduced, along with its essential properties. This operator integrates these separate groups while preserving the relationships between the attributes within each group. Furthermore, the partitioned Hamy mean (PHM) and the PDHM operators are also constructed in the generalized orthopair fuzzy environment, namely the q-rung orthopair fuzzy PHM (q-ROFPHM), the q-rung orthopair fuzzy PDHM (q-ROFPDHM), and their weighted forms. Their essential properties are verified to ensure the validity of the proposed aggregation operators (AOs). Subsequently, a new MAGDM approach is developed, employing the proposed AOs. The MAGDM problem of selecting the best person is examined. Moreover, the research includes a sensitivity analysis in three directions and a comparative analysis of the proposed MAGDM approach with five different approaches. The findings indicate that applying attribute partitioning in the proposed approach mitigates the adverse impact of irrelevant attributes, leading to more feasible and reliable outcomes. Additionally, a practical case study focuses on selecting a suitable industry for investment among the five available options. This case study demonstrates the approach's effectiveness by considering five distinct qualities and results that make the Internet industry the best place to invest. Furthermore, a comparative analysis with four similar papers is also performed, indicating that the developed method's results are more reliable and consistent. [ABSTRACT FROM AUTHOR]

Petroleum is the main power of automobiles, yet the environmental pollution it brings has caused globally. The promotion of new energy vehicles (NEVs) is effective. Even though the governments have introduced various supports for the popularization of NEVs, many enterprises and individuals continue to drive gas vehicles as they are poorly informed about them and cannot choose the right products. This paper proposes a categorization and ranking model of NEVs over three-way decisions (TWD) to tackle the problem. Picture fuzzy sets serve as a valid tool to describe uncertainty and fuzziness information. At first, the attribute weights are ascertained with the indifference threshold-based attribute ratio analysis (ITARA) method improved by the picture fuzzy distance. Then, the public weight picture fuzzy data envelopment analysis (DEA) which is enhanced by the picture fuzzy aggregation operator is employed for the conditional probability of decision units. Third, updated picture fuzzy TWD is utilized for the categorization and ranking. Fourth, the enterprise NEVs selection case is tested for the model. Later, comparative analysis with the classical methods illustrates that the proposed method yields accurate and reliable decisions. Finally, the robustness of the model is demonstrated by sensitivity analysis. [ABSTRACT FROM AUTHOR]

During the transitional phase spanning from the realm of fuzzy logic to the realm of neutrosophy, a multitude of hybrid models have emerged, each surpassing its predecessor in terms of superiority. Given the pervasive presence of indeterminacy in the world, a higher degree of precision is essential for effectively handling imprecision. Consequently, more sophisticated variants of neutrosophic sets (NSs) have been conceived. The key objective of this paper is to introduce yet another variant of NS, known as the q-rung orthopair fuzzy-valued neutrosophic set (q-ROFVNS). By leveraging the extended spatial range offered by q-ROFS, q-ROFVNS enables a more nuanced representation of indeterminacy and inconsistency. Our endeavor commences with the definitions of q-ROFVNS and q-ROFVN numbers (q-ROFVNNs). Then, we propose several types of score and accuracy functions to facilitate the comparison of q-ROFVNNs. Fundamental operations of q-ROFVNSs and some algebraic operational rules of q-ROFVNNs are also provided with their properties, substantiated by proofs and elucidated through illustrative examples. Drawing upon the operational rules of q-ROFVNNs, the q-ROFVN weighted average operator (q-ROFVNWAO) and q-ROFVN weighted geometric operator (q-ROFVNWGO) are proposed. Notably, we present the properties of these operators, including idempotency, boundedness and monotonicity. Furthermore, we emphasize the applicability and significance of the q-ROFVN operators, substantiating their utility through an algorithm and a numerical application. To further validate and evaluate the proposed model, we conduct a comparative analysis, examining its accuracy and performance in relation to existing models. [ABSTRACT FROM AUTHOR]

Advancement in mobile phone (MP) technology has revolutionized the lifestyle. In recent years, we observed that MP technology had been involved in almost all aspects of life, such as communication purposes, e-commerce, mobile baking, and social media connectivity. So, it becomes a hot research topic to select the best MP that fulfills the desired feathers requirement. In this paper, the expert's familiarity with the examined objects is factored into the initial judgments under the T-spherical fuzzy sets (T-SFSs) environment. The T-SFS is the extension of the picture fuzzy (PF) set (PFS), which gives wider scope for finding the most precise options than existing fuzzy frameworks. The multiattribute decision-making (MADM) is a common and valuable method for aggregating information. For MADM, various aggregation operators (AOs) have been created over the years. The article introduces the newly proposed approach T-spherical fuzzy (T-SF) confidence level weighted averaging T − SFWA c and T-SF confidence level weighted geometric T − SFWG c . Also, some desired properties of AOs are discussed, and the T-SF entropy measure is introduced for selecting the weight criteria. A MADM framework is introduced, on the behalf of proposed operators. The proposed MADM framework is applied to solve the real-life example of consumers' preferences to show effectiveness and practicality. Lastly, the developed framework is set side by side with other prevailing approaches to demonstrate the superiority and significance of other existing AOs. [ABSTRACT FROM AUTHOR]

Intuitionistic fuzzy (IF) information aggregation in multi-criteria decision making (MCDM) is a substantial stream that has attracted significant research attention. There are various IF aggregation operators have been suggested for extracting more informative data from imprecise and redundant raw information. However, some of the aggregation techniques that are currently being applied in IF environments are non-monotonic with respect to the total order, and suffer from high computational complexity and inflexibility. It is necessary to develop some novel IF aggregation operators that can surpass these imperfections. This paper aims to construct some IF aggregation operators based on Yager's triangular norms to shed light on decision-making issues. At first, we present some novel IF operations such as Yager sum, Yager product and Yager scalar multiplication on IF sets. Based on these new operations, we propose the IF Yaeger weighted geometric operator and the IF Yaeger ordered weighted geometric operator, and prove that they are monotone with respect to the total order. Then, the focus on IF MCDM have motivated the creation of a new MCDM model that relies on suggested operators. We show the applicability and validity of the model by using it to select the most influential worldwide supplier for a manufacturing company and evaluate the most efficient method of health-care disposal. In addition, we discuss the sensitivity of the proposed operator to decision findings and criterion weights, and also analyze it in comparison with some existing aggregation operators. The final results show that the proposed operator is suitable for aggregating both IF information on "non-empty lattice" and IF data on total orders. [ABSTRACT FROM AUTHOR]

Linguistic q-rung orthpair fuzzy sets (Lq-ROFSs) can facilitate describing the uncertainty and the vagueness information existing in the real world. Based on the advantages of Lq-ROFSs, this paper innovatively puts forward a new method to solve the multi-attribute group decision-making (MAGDM) problems when the attribute weight is completely unknown, and proves the feasibility and effectiveness of this method through illustrative examples. Firstly, we propose the linguistic q-rung orthopair fuzzy generalized power average (Lq-ROFGPA) operator, which considers not only the importance of the data itself, but also the interaction between the data, and prove its properties. In particular, the linguistic q-rung orthopair fuzzy weighted generalized power average (Lq-ROFWGPA) operator takes into account the weight between data, which can better aggregate evaluation information. Then, we introduce decision making trial and evaluation laboratory (DEMATEL) method of the linguistic q-rung orthpair fuzzy numbers (Lq-ROFNs) to analyze the causal relationship and key elements of complex systems. Based on DEMATEL method, we further develop a weight model to calculate the attribute weights, which can make up for the deficiency which is the influence of the interaction between attributes that the existing weight determination method for Lq-ROFNs does not consider. Finally, we present a new MAGDM method based on the Lq-ROFWGPA operator and DEMATEL method. Further, several practical examples are given to illustrate the effectiveness and superiority of this new method in comparison with other existing MAGDM methods. [ABSTRACT FROM AUTHOR]

Probabilistic interval ordering, as a helpful tool for expressing positive and negative information, can effectively address multi-attribute decision-making (MADM) problems in reality. However, when dealing with a significant number of decision-makers and decision attributes, the priority relationships between different attributes and their relative importance are often neglected, resulting in deviations in decision outcomes. Therefore, this paper combines probability interval ordering, the prioritized aggregation (PA) operator, and the Gauss–Legendre algorithm to address the MADM problem with prioritized attributes. First, considering the significance of interval priority ordering and the distribution characteristics of attribute priority, the paper introduces probability interval ordering elements that incorporate attribute priority, and it proposes the probabilistic interval ordering prioritized averaging (PIOPA) operator. Then, the probabilistic interval ordering Gauss–Legendre prioritized averaging operator (PIOGPA) is defined based on the Gauss–Legendre algorithm, and various excellent properties of this operator are explored. This operator considers the priority relationships between attributes and their importance level, making it more capable of handling uncertainty. Finally, a new MADM method is constructed based on the PIOGPA operator using probability intervals and employs the arithmetic–geometric mean (AGM) algorithm to compute the weight of each attribute. The feasibility and soundness of the proposed method are confirmed through a numerical example and comparative analysis. The MADM method introduced in this paper assigns higher weights to higher-priority attributes to establish fixed attribute weights, and it reduces the impact of other attributes on decision-making results. It also utilizes the Gauss AGM algorithm to streamline the computational complexity and enhance the decision-making effectiveness. [ABSTRACT FROM AUTHOR]

As dual hesitant fuzzy sets can express the uncertainty of data efficiently, the aggregation of dual hesitant fuzzy information plays an important role in both theory and application. However, some existing dual hesitant fuzzy aggregation operators are not rigorous enough actually. In this note, we show that some theorems in an earlier paper by Ju et al. [1] (Journal of Intelligent & Fuzzy Systems 27 (2014) 2481–2495) are not correct, i.e., the dual hesitant fuzzy Hamacher weighted averaging operator (DHFHWA) and some other aggregation operators proposed by Ju et al. don't satisfy idempotency and boundedness. Therefore, the purpose of this paper is to make researchers aware of that some aggregation operators in literature [1] are flawed and limited for many applications. [ABSTRACT FROM AUTHOR]

It is difficult to describe the hesitation and uncertainty of experts by single-valued information, and the differences in the importance of attributes are often ignored during the decision-making process. This paper introduces the probability and interval values into Fermatean hesitant fuzzy set (FHFS) and creatively proposes the probabilistic interval-valued Fermatean hesitant fuzzy set (PIVFHFS) to deal with information loss. This new fuzzy set allows decision makers to use interval-valued information with probability to express their quantitative evaluation, which broadens the range of information expression, effectively reflects the important degree of different membership degrees, and can describe uncertain information more completely and accurately. Under the probabilistic interval-valued Fermatean hesitant fuzzy environment, several new aggregation operators based on Hamacher operation are proposed, including the probabilistic interval-valued Fermatean hesitant fuzzy Hamacher weighted averaging (PIVFHFHWA) operator and geometric (PIVFHFHWG) operator, and their basic properties and particular forms are studied. Then, considering the general correlation between different attributes, this paper defines the probabilistic interval-valued Fermatean hesitant fuzzy Hamacher Choquet integral averaging (PIVFHFHCIA) operator and geometric (PIVFHFHCIG) operator and discusses related properties. Finally, a multi-attribute decision-making (MADM) method is presented and applied to the decision-making problem of reducing carbon emissions of manufacturers in the supply chain. The stability and feasibility of this method are demonstrated by sensitivity analysis and comparative analysis. The proposed new operators can not only consider the correlation between various factors but also express the preference information of decision makers more effectively by using probability, thus avoiding information loss in decision-making progress to some extent. [ABSTRACT FROM AUTHOR]

The present work endeavours to delve into the relationship between life satisfaction, coping behaviour for stress, and innovative work behaviour. To do so, the current work utilizes a q-rung orthopair fuzzy (q-ROF) based group decision making framework. The paper uses the framework to measure three aspects, life satisfaction (LS), stress coping (SC) and work behaviour (WB) from the past studies. A questionnaire with a five-point Likert scale was administered to the target respondents. For each respondent, the responses received from each respondent were aggregated using the q-ROF Einstein weighted average (q-ROFEWA) as the aggregation operator (AO). The relationships were then examined using the Mann Whitney U test. It was observed that LS has a positive relationship with SC, which also maintains a positive linkage with WB. The present paper provides useful insights for talent management by providing a framework for the assessment of productivity while keeping track of mental health. [ABSTRACT FROM AUTHOR]

Q-rung orthopair fuzzy sets have been proven to be highly effective at handling uncertain data and have gained importance in decision-making processes. Torra's hesitant fuzzy model, on the other hand, offers a more generalized approach to fuzzy sets. Both of these frameworks have demonstrated their efficiency in decision algorithms, with numerous scholars contributing established theories to this research domain. In this paper, recognizing the significance of these frameworks, we amalgamated their principles to create a novel model known as Q-rung orthopair hesitant fuzzy sets. Additionally, we undertook an exploration of Aczel–Alsina aggregation operators within this innovative context. This exploration resulted in the development of a series of aggregation operators, including Q-rung orthopair hesitant fuzzy Aczel–Alsina weighted average, Q-rung orthopair hesitant fuzzy Aczel–Alsina ordered weighted average, and Q-rung orthopair hesitant fuzzy Aczel–Alsina hybrid weighted average operators. Our research also involved a detailed analysis of the effects of two crucial parameters: λ , associated with Aczel–Alsina aggregation operators, and N, related to Q-rung orthopair hesitant fuzzy sets. These parameter variations were shown to have a profound impact on the ranking of alternatives, as visually depicted in the paper. Furthermore, we delved into the realm of Wireless Sensor Networks (WSN), a prominent and emerging network technology. Our paper comprehensively explored how our proposed model could be applied in the context of WSNs, particularly in the context of selecting the optimal gateway node, which holds significant importance for companies operating in this domain. In conclusion, we wrapped up the paper with the authors' suggestions and a comprehensive summary of our findings. [ABSTRACT FROM AUTHOR]

Nowadays career choosing is a very difficult job for many students. This paper primarily addresses the concerns of those students who face difficulty in choosing the right career option for themselves, using multi-attribute group decision-making (MAGDM) methodologies based on CRITIC (Criteria Importance Through Inter criteria Correlation) and EDAS (Evaluation based on Distance from Average Solution) strategies under the single-valued neutrosophic set (SVNS) environment. First, the CRITIC strategy is used to calculate the weights of the attributes and then these weights are used to develop EDAS strategy in the SVNS environment. Since the usage of the geometric operator CRITIC-EDAS has not before been documented in the literature, this study is distinctive. A realistic example of commerce students' career selection problem is discussed. [ABSTRACT FROM AUTHOR]

Due to the complexity and uncertainty of decision-making, probabilistic linguistic term sets (PLTSs) are currently important tools for qualitative evaluation of decision-makers. The asymmetry of evaluation information can easily lead to the loss of subjective preference information for decision-makers, and the existing operation of decision-maker evaluation information fusion operators is difficult to solve this problem. To solve such problems, this paper proposes some new operational methods for PLTSs based on Dombi T-conorm and T-norm. Considering the interrelationships between the input independent variables of PLTSs, the probabilistic linguistic weighted Dombi Bonferroni mean Power average (PLWDBMPA) operators are extended and the properties of these aggregation operators are proposed. Secondly, the PLWDBMPA operator is used to fuse the evaluation information of decision-makers, avoiding the loss of decision information as much as possible. This paper uses social media platforms and web crawler technology to obtain online comments from users on decision-making to obtain the public's attitude towards decision events. TF-IDF and Word2Vec are used to calculate the weight of alternatives on each attribute. Under traditional group decision-making methods and integrating the wisdom of the public, a novel multi-attribute group decision-making method based on TODIM method is proposed. Finally, the case study of Turkey earthquake shelter selection proves this method is scientific and effective. Meanwhile, the superiority of this method was further verified through comparisons with the PL-TOPSIS, PLWA, SPOTIS and PROMETHEE method. [ABSTRACT FROM AUTHOR]

In this paper, we establish the matching relation between implication operator and aggregation operator, which provides a new solution for the design and construction of multi-rule fuzzy inference system. Firstly, according to the definition and monotonicity of implication operator, a new classification method of implication operator is proposed, and then the fuzzy inference process using different implication operators is classified. Then, dynamic maximum aggregation operator and dynamic minimum aggregation operator are proposed. Based on the compositional rule of inference (CRI) method, a matching method and basis of implication operator and aggregation operator for fuzzy inference systems is given and illustrated with examples. Finally, the applicability of the proposed method in this paper is further illustrated by comparing the method with existing methods in the literature and using the nearness degree as an evaluation index. [ABSTRACT FROM AUTHOR]

This paper aims to present Bipolar valued probabilistic hesitant fuzzy sets (BVPHFSs) by combining bipolar fuzzy sets and probabilistic hesitant fuzzy sets (PHFSs). PHFSs are a strong version of hesitant fuzzy sets (HFSs) in terms of evaluated as probabilistic of each element. Probabilistic hesitant fuzzy sets (PHFSs) are a set structure that argues that each alternative should be evaluated probabilistically. In this framework, the proposed cluster allows probabilistic evaluation of decision- makers' opinions as negative. Thus, this case proposes flexibility about selection of an element and aids to overcome with noise channels. Furthermore, some new aggregation operators are discussed called bipolar valued probabilistic hesitant fuzzy weighted average operator (BVPHFWA), Generalized bipolar valued probabilistic hesitant fuzzy weighted average operator (GBVPHFWA), bipolar valued probabilistic hesitant fuzzy weighted geometric operator (BVPHFWG), Generalized bipolar valued probabilistic hesitant fuzzy weighted geometric operator (GBVPHFWG), bipolar valued probabilistic hesitant fuzzy hybrid weighted arithmetic and geometric operator (BVPHFHWAG) and Generalized bipolar valued probabilistic hesitant fuzzy hybrid weighted arithmetic and geometric (GBVPHFHWAG) and some basic properties are presented. A score function is defined ranking alternatives. Moreover, two different algorithms are put forward with helping to TOPSIS method and by using aggregation operators over BVPHFSs. The validity of proposed operators are analyzed with an example and results are compared in their own. [ABSTRACT FROM AUTHOR]

A Single-valued neutrosophic set (SVNS) has recently been explored as a comprehensive tool to assess uncertain information due to varied human cognition. This notion stretches the domain of application of the classical fuzzy set and its extended versions. Various comparison measures based on SVNSs like distance measure, similarity measure, and, divergence measure have practical significance in the study of clustering analysis, pattern recognition, machine learning, and computer vision-related problems. Existing measures have some drawbacks in terms of precision and exclusion of information and produce unreasonable results in categorization problems. In this paper, we propose a generic method to define new divergence measures based on common aggregation operators and discuss some algebraic properties of the proposed divergence measures. To further appreciate the proposed divergence measures, their application to pattern recognition has been investigated in conjunction with the prominent existing comparison measures based on SVNSs. The comparative assessment sensitivity analysis of the proposed measures establishes their edge over the existing ones because of appropriate classification results. [ABSTRACT FROM AUTHOR]

One of the main problems faced by resilient supply chain management is how to solve the problem of supplier selection, which is a typical multi-attribute decision-making (MADM) problem. Given the complexity of the current decision-making environment, the primary influence of this paper is to propose the theory of Dombi operational laws based on complex intuitionistic fuzzy (CIF) information. Moreover, we examined the theory of CIF Dombi prioritized averaging (CIFDPA) and CIF weighted Dombi prioritized averaging (CIFWDPA), where these operators are the modified version of the prioritized aggregation operators and Dombi aggregation operators for fuzzy, intuitionistic fuzzy, complex fuzzy and complex intuitionistic fuzzy information. Some reliable properties for the above operators are also established. Furthermore, to state the art of the proposed operators, an application example in the presence of the invented operators is evaluated for managing resilient green supplier selection problems. Finally, through comparative analysis with mainstream technologies, we provide some mechanism explanations for the proposed method to show the supremacy and worth of the invented theory. [ABSTRACT FROM AUTHOR]

The Fuzzy-Weighted Zero-Inconsistency (FWZIC) and Fuzzy-Decision-by-Opinion-Score-Method (FDOSM) are considered the recent advance methods. FDOSM generates a ranking for possible alternatives, while FWZIC produces a weight for criterion. Keeping up with the stream of academic publications on the FDOSM and FWZIC methods is complicated. This study aims to provide a comprehensive review of the literature on the latest advanced methods of MCDM in order to reorganize the findings of the previous literature and provide decisive evidence for ongoing research and future studies. Based on previous literature, the current study used the Prisma method to collect data from multiple databases such as IEEE Xplore®, ScienceDirect, and Web of Science. There were 45 papers discovered relevant to this subject; however, only 23 studies were relevant for the FDOSM & FWZIC study. The results included theoretical and practical implications. Theoretically, additions of new aggregation operators or usage of new fuzzy sets in the FDOSM & FWZIC model to solve the uncertainty problem are the key obstacles. Practically, agriculture and architectural fields are considered to be a hotspot of research. Finally, a number of potential points for future research to develop methods with high certainty and low ambiguity are presented. [ABSTRACT FROM AUTHOR]

The picture fuzzy set (PFS) is a more frequent platform for describing the degree of positive, neutral, and negative membership functions that generalizes the concept of fuzzy sets (FSs) and intuitionistic fuzzy sets (IFSs). Neutrality is a crucial component of PFS, and the score function plays a crucial role in ranking the alternatives in decision-making situations. In the decision-making process, some researchers concentrate on the various aggregation operators' development while ignoring the development of score functions. This factor causes several errors in the existing score function. If there are two separate picture fuzzy numbers (PFNs), there should be two different scores or accuracy values. Some researchers failed to rank the alternatives when the score and accuracy values for various PFNs were equal. To overcome the shortcomings, we proposed the perfect score function in this paper for ranking PFNs and introduced strong and weak PFSs. The shortcoming of the existing score function in PFNs has been highlighted in this paper. Furthermore, the decision-making approach has been depicted based on the proposed score function, and real-world applications have been shown by ranking the COVID-19 affected regions to demonstrate its efficacy. [ABSTRACT FROM AUTHOR]

As an extension of the concepts of fuzzy set and intuitionistic fuzzy set, the concept of Pythagorean fuzzy set better models some real life problems. Distance, entropy, and similarity measures between Pythagorean fuzzy sets play important roles in decision making. In this paper, we give a new entropy measure for Pythagorean fuzzy sets via the Sugeno integral that uses fuzzy measures to model the interaction between criteria. Moreover, we provide a theoretical approach to construct a similarity measure based on entropies. Combining this theoretical approach with the proposed entropy, we define a distance measure that considers the interaction between criteria. Finally, using the proposed distance measure, we provide an extended Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) for multi-criteria decision making and apply the proposed technique to a real life problem from the literature. Finally, a comparative analysis is conducted to compare the results of this paper with those of previous studies in the literature. [ABSTRACT FROM AUTHOR]

This paper aims to propose a novel multi‐attribute group decision‐making (MAGDM) method based on linguistic Pythagorean fuzzy copula extended power average operator. Existing researches under linguistic Pythagorean fuzzy environment lack of the ability to handle with extreme values and the flexible operational rules. To fill these two gaps, this paper first provides the definition of Archimedean copula and co‐copula operational rules under linguistic Pythagorean fuzzy environment, which can reflect the connection among arguments and provide more choices for experts to express their preferences. Then, we gather the extended power average (EPA) operator to present some new aggregation operators, which can reduce the negative influence of extreme evaluation values. To show the application of the proposed method to MAGDM problems, we apply it to handle a case of takeout O2O platform assessment problem. The numerical case and comparative analysis with other existing methods illustrate that our proposed method is more scientific and flexible. [ABSTRACT FROM AUTHOR]

Novel methods for multiple attribute decision-making problems are presented in this paper using Type-Ⅱ Fermatean normal numbers. Type-Ⅱ Fermatean fuzzy sets are developed by further generalizing Fermatean fuzzy sets and neutrosophic sets. The Type-Ⅱ Fermatean fuzzy sets with basic aggregation operators are constructed. The concept of a Type-Ⅱ Fermatean normal number is compatible with both commutative and associative rules. This article presents a new proposal for Type-Ⅱ Fermatean normal weighted averaging, Type-Ⅱ Fermatean normal weighted geometric averaging, Type-Ⅱ generalized Fermatean normal weighted averaging, and Type-Ⅱ generalized Fermatean normal weighted geometric averaging. Furthermore, these operators can be used to develop an algorithm that solves MADM problems. Applications for the Euclidean distance and Hamming distances are discussed. Finally, the sets that arise as a result of their connection to algebraic operations are emphasized in our discourse. Examples of real-world applications of enhanced Hamming distances are presented. A sensor robot's most important components are computer science and machine tool technology. Four factors can be used to evaluate the quality of a robotics system: resolution, sensitivity, error and environment. The best alternative can be determined by comparing expert opinions with the criteria. As a result, the proposed models' outcomes are more precise and closer to integer number δ . To demonstrate the applicability and validity of the models under consideration, several existing models are compared with the ones that have been proposed. Novel methods for multiple attribute decision-making problems are presented in this paper using Type-Ⅱ Fermatean normal numbers. Type-Ⅱ Fermatean fuzzy sets are developed by further generalizing Fermatean fuzzy sets and neutrosophic sets. The Type-Ⅱ Fermatean fuzzy sets with basic aggregation operators are constructed. The concept of a Type-Ⅱ Fermatean normal number is compatible with both commutative and associative rules. This article presents a new proposal for Type-Ⅱ Fermatean normal weighted averaging, Type-Ⅱ Fermatean normal weighted geometric averaging, Type-Ⅱ generalized Fermatean normal weighted averaging, and Type-Ⅱ generalized Fermatean normal weighted geometric averaging. Furthermore, these operators can be used to develop an algorithm that solves MADM problems. Applications for the Euclidean distance and Hamming distances are discussed. Finally, the sets that arise as a result of their connection to algebraic operations are emphasized in our discourse. Examples of real-world applications of enhanced Hamming distances are presented. A sensor robot's most important components are computer science and machine tool technology. Four factors can be used to evaluate the quality of a robotics system: resolution, sensitivity, error and environment. The best alternative can be determined by comparing expert opinions with the criteria. As a result, the proposed models' outcomes are more precise and closer to integer number . To demonstrate the applicability and validity of the models under consideration, several existing models are compared with the ones that have been proposed. [ABSTRACT FROM AUTHOR]

In 2014, Hu introduced the concept of three-way decision spaces and axiomatic definition of decision evaluation functions. In three-way decision spaces, decision evaluation function satisfies minimum element axiom, monotonicity axiom and complement axiom. Since then, the research on construction method of decision evaluation functions from commonly used binary aggregation functions becomes a research hotspot. Meanwhile, uninorms, as one class of binary aggregation functions, have been successfully applied in various application problems, such as in decision making, image processing, data mining, etc. This paper continues to consider this research topic and mainly explores the new construction methods of decision evaluation functions based on uninorms. Firstly, we show two novel transformation methods from semi-decision evaluation functions to decision evaluation functions based on uninorms. Secondly, using known semi-decision evaluation functions, we give some new construction methods of semi-decision evaluation functions. Thirdly, we give some novel construction methods of decision evaluation functions and semi-decision evaluation functions related to fuzzy sets, interval-valued fuzzy sets, fuzzy relations and hesitant fuzzy sets. Based on them, decision maker can obtain more useful decision evaluation functions, thereby more choices can be used for realistic decision-making problems. Finally, we consider two real evaluation problems to illustrate the results obtained in this paper. The three-way decisions results of evaluation problem show that the construction method proposed in this paper is superior to some existing construction methods under some conditions. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to develop some aggregating operators for Picture fuzzy sets (PFS) by integrating power average (PA) and Muirhead mean (MM) operators. This paper develops Picture fuzzy power Muirhead mean (PFPMM), Picture fuzzy weighted power Muirhead mean (PFWPMM), Picture fuzzy dual power Muirhead mean (PFDPMM) and Picture fuzzy weighted dual power Muirhead mean (PFWDPMM) operators along with some desirable properties and special cases. Some advantages of developed operators are that they define the interrelationship between all aggregated values and lead to a flexible aggregation process through a parameter vector. Further, a multi-attribute decision making (MADM) problem based on proposed operators has been presented. To exemplify the availability and practicability of the proposed study, a financial investment risk problem in an enterprise is solved numerically. A sensitivity analysis is conducted to examine the effect of different values of parameters on aggregated values, while a comparative analysis is carried out to compare the results with some other existing operators. [ABSTRACT FROM AUTHOR]

Pooling the opinions of the decision makers about premier alternative from a list of given choices is the most crucial phenomenon theory of decision making. The MSM operator is an effective approach and can identify the collective connection among various input viewpoints. So, tacking the fully benefit of MSM operator, this paper presents a new novel in depth investigation of MSM in context of Neutrosophic fuzzy variables. Initially we developed the structure of One-dimension uncertain linguistic interval valued neutrosophic fuzzy variables, deliberate their fundamental properties along with meaningful laws. Moreover, we encompass the MSM operator to the extent of one dimensional uncertain-linguistic Neutrosophic fuzzy variables and introduced some novel aggregations operators including one-dimensional uncertain linguistic interval-valued Neutrosophic fuzzy, weighted fuzzy and ordered weighted fuzzy McLaurin symmetric mean operator. The practical utilization of the proposed aggregation operators in business analytic are also included in the paper. In last comparison is made between current vs old studies which proved solidity and reliability of the new operator's vs existing operators in the literature. [ABSTRACT FROM AUTHOR]

Consolidating cubical fuzzy numbers (CFNs) is essential in an uncertain decision-making process. This study focuses on creating innovative cubical fuzzy aggregation operators based on the newly proposed Einstein operational laws, utilizing the Bonferroni mean function to capture the interrelationships among the aggregated CFNs. The first contribution of this paper is introducing a novel cubical fuzzy Einstein Bonferroni mean averaging operator. Building upon this operator, we extend our research to develop cubical fuzzy Einstein Bonferroni mean weighted, ordered weighted, and hybrid averaging operators, taking into account the weights of the aggregated CFNs. To ensure their effectiveness, we thoroughly investigate the desirable properties of these proposed operators. Furthermore, we leverage the introduced operators to establish a new approach known as the cubical fuzzy linear assignment method, which proves valuable in resolving multiple criteria group decision-making problems. As a practical demonstration of the method's utility, we apply it to address a real-life challenge: identifying the optimal location for constructing a wind power plant under a cubical fuzzy environment. To validate the effectiveness of our approach, we compare its results with those obtained using existing methods from the literature. Additionally, we conduct a statistical analysis to visualize the correlative conjunction between the ranking outcomes obtained by different operators [ABSTRACT FROM AUTHOR]

One of the hottest areas for applying the solutions currently available is the internet of things-based smart housing society architecture and its uncertainty analysis. When intelligent parking, waste management, public transportation, public safety, and other automatic methods for housing society's growth were implemented, it became even more crucial. An intelligent, smart system is necessary to manage these problems and provide smooth services. Additionally, it will be helpful in reducing issues with time waste and societal safety. However, the issue comes up when describing accurate, approximate, or questionable parking, transit, safety, and waste management areas. This paper discusses several mathematical solutions for the smart housing society that use fuzzy rough sets, probabilistic hesitant fuzzy sets, and their extensions with neutrosophic sets. For further growth, a few studies on the graphic display of the evolution of the smart housing society are also considered. The rough set theory can be useful when dealing with imprecise, incomplete, or indeterminate data sets. The core contribution of this work is the construction of a novel generalized notion of a single-valued neutrosophic probabilistic hesitant fuzzy rough set (SV-NPHFRS), which is a hybrid structure of the single-valued neutrosophic set, the probabilistic hesitant fuzzy set, and the rough set. In contrast to the present literature, the underlying idea of SV-NPHFRS is that it is a powerful mathematical tool for managing uncertainty and imperfect information. This method is particularly beneficial when there are a number of competing criteria to consider. The aggregation technique plays an important role in decision-making concerns, especially when more competing criteria are present. In the study's comparison phase, the suggested decision support system is compared to relevant existing approaches. The results suggest that, in terms of choice flexibility, the suggested technique has the potential to outperform the drawbacks of the current decision-making tools. The proposed study is expected to be useful for a number of researchers conducting future work on housing societies, waste management, public safety diagnostics, and hybridization. [ABSTRACT FROM AUTHOR]